POLYNOMIAL REGRESSIONS
To do polynomial regressions in matlab, you need to use the "polyfit"
function. To use it, you must enter your data into variables. For
example:
x = [1 2 3 4 5 6 7 8];
y = [1 4 9 16 25 36 49 64];
Then, to do the regression, you'd do something like:
c = polyfit(x,y,3);
This would fit it to a third order polynomial; to have it fit to a
higher order polynomial, you could just change the last argument to what
you want.
Then to see the fit polynomials in the example above, you can just type:
c
In this case, Matlab returns:
0.0000 1.0000 0.0000 -0.0000
These are the coefficients in descending power of x, of the n-th order
polynomial that fits the vector y to x.
If you would like to plot both the data AND the result of fitting, you
can use the polyval function to do so. Type:
newy = polyval(c,x);
newy will be the vector containing the values of X evalated using the
coefficients of the polynomial that fits y to x. To plot both the data
and the fitted data, type:
plot(x,y,x,newy)
You can also find a polynomial in x and y that fits a given set of data
using the "poly2fit" and "poly2val" commands. Usage of these commands is
similar to "polyfit" and "polyval", except that x,y and z are matrices.
You can use the "meshgrid" command to transform a domain specified by two
vectors X and Y, into array form. Then
c = poly2fit(x,y,z,3)
returns the coefficients of the fitted polynomial in descending powers
of x and y.
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